Ancient Indian mathematical text at Oxford's Bodleian Libraries revealed to be centuries older than previously thought

The origin of the symbol zero has long been one of the world's greatest mathematical mysteries. Today, new carbon dating research commissioned by the University of Oxford's Bodleian Libraries into the ancient Indian Bakhshali manuscript, held at the Bodleian, has revealed it to be hundreds of years older than initially thought, making it the world’s oldest recorded origin of the zero symbol that we use today.

The surprising results of the first ever radiocarbon dating conducted on the Bakhshali manuscript, a seminal mathematical text which contains hundreds of zeroes, reveal that it dates from as early as the 3rd or 4th century - approximately five centuries older than scholars previously believed. This means that the manuscript in fact predates a 9th-century inscription of zero on the wall of a temple in Gwalior, Madhya Pradesh, which was previously considered to be the oldest recorded example of a zero used as a placeholder in India. The findings are highly significant for the study of the early history of mathematics.

The zero symbol that we use today evolved from a dot that was used in ancient India and can be seen throughout the Bakhshali manuscript. The dot was originally used as a 'placeholder', meaning it was used to indicate orders of magnitude in a number system – for example, denoting 10s, 100s and 1000s.

While the use of zero as a placeholder was seen in several different ancient cultures, such as among the ancient Mayans and Babylonians, the symbol in the Bakhshali manuscript is particularly significant for two reasons. Firstly, it is this dot that evolved to have a hollow centre and became the symbol that we use as zero today. Secondly, it was only in India that this zero developed into a number in its own right, hence creating the concept and the number zero that we understand today - this happened in 628 AD, just a few centuries after the Bakhshali manuscript was produced, when the Indian astronomer and mathematician Brahmagupta wrote a text called Brahmasphutasiddhanta, which is the first document to discuss zero as a number.

Although the Bakhshali manuscript is widely acknowledged as the oldest Indian mathematical text, the exact age of the manuscript has long been the subject of academic debate. The most authoritative academic study on the manuscript, conducted by Japanese scholar Dr Hayashi Takao, asserted that it probably dated from between the 8th and the 12th century, based on factors such as the style of writing and the literary and mathematical content. The new carbon dating reveals that the reason why it was previously so difficult for scholars to pinpoint the Bakhshali manuscript’s date is because the manuscript, which consists of 70 fragile leaves of birch bark, is in fact composed of material from at least three different periods.

Marcus du Sautoy, Professor of Mathematics at the University of Oxford, said:

'Today we take it for granted that the concept of zero is used across the globe and is a key building block of the digital world. But the creation of zero as a number in its own right, which evolved from the placeholder dot symbol found in the Bakhshali manuscript, was one of the greatest breakthroughs in the history of mathematics.

'We now know that it was as early as the 3rd century that mathematicians in India planted the seed of the idea that would later become so fundamental to the modern world. The findings show how vibrant mathematics have been in the Indian sub-continent for centuries.'

Richard Ovenden, Bodley's Librarian, said:

'Determining the date of the Bakhshali manuscript is of vital importance to the history of mathematics and the study of early South Asian culture and these surprising research results testify to the subcontinent's rich and longstanding scientific tradition. The project is an excellent example of the cutting-edge research conducted by the Bodleian’s Heritage Science team, together with colleagues across Oxford University, which uncovers new information about the treasures in our collections to help inform scholarship across disciplines.'

The Bakhshali manuscript was found in 1881, buried in a field in a village called Bakhshali, near Peshawar, in what is now a region of Pakistan. It was found by a local farmer and was acquired by the Indologist AFR Hoernle, who presented it to the Bodleian Library in 1902, where it has been kept since.

A folio from the Bakhshali manuscript will go on public display at the Science Museum in London as a centrepiece of the major exhibition Illuminating India: 5000 Years of Science and Innovation, opening 4 October 2017. The exhibition will celebrate India’s central role in the history of science and technology by exploring its influential contributions to subjects as diverse as space exploration, mathematics, communication and engineering.